# Reshuffled-ΔZ Permutation Placebo

**Reviewer Issue 3.2**: Strengthen placebo by randomly permuting demographic
distances across bilateral pairs within each year.

## Results (1000 permutations)

| Statistic | Value |
|-----------|-------|
| Actual h=2 Investment/GDP β | 0.69170** |
| Actual p-value | 0.0437 |
| Shuffled mean β | 0.60112 |
| Shuffled SD | 0.05237 |
| Actual / shuffled SD | 13.21 |
| Permutation p-value | 0.0400 |
| N permutations | 1000 |

## Distribution of shuffled h=2 coefficients

- P5: 0.51715
- P25: 0.56432
- P50: 0.59962
- P75: 0.63761
- P95: 0.68614
- **Actual**: 0.69170

## Interpretation

The actual h=2 investment coefficient lies in the extreme tail of the
permutation distribution, confirming that the J-curve is specific to
the actual bilateral demographic pairing, not an artifact of the gravity
aggregation procedure.
